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Mirrors > Home > ILE Home > Th. List > orim1d | GIF version |
Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.) |
Ref | Expression |
---|---|
orim1d.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
orim1d | ⊢ (𝜑 → ((𝜓 ∨ 𝜃) → (𝜒 ∨ 𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orim1d.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | idd 21 | . 2 ⊢ (𝜑 → (𝜃 → 𝜃)) | |
3 | 1, 2 | orim12d 700 | 1 ⊢ (𝜑 → ((𝜓 ∨ 𝜃) → (𝜒 ∨ 𝜃))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ wo 629 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: pm2.38 716 pm2.73 719 pm2.74 720 pm2.8 723 pm2.82 725 unss1 3112 acexmidlemcase 5507 nn0ge2m1nn 8242 |
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